%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET076-6 : TPTP v9.2.1. Bugfixed v2.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n012.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:47:16 AM UTC 2026 % Result : Unsatisfiable 0.15s 0.40s % Output : Proof 0.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SET076-6 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 14:51:03 EDT 2026 % 0.07/0.25 % CPUTime : % 0.15/0.34 %----Proving TF0_NAR, FOF, or CNF % 0.15/0.35 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.15/0.40 % SZS status Unsatisfiable % 0.15/0.40 % SZS output start Proof % 0.15/0.40 ( % 0.15/0.40 (declare-sort $$unsorted 0) % 0.15/0.40 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.15/0.40 (declare-const tptp.operation (-> $$unsorted Bool)) % 0.15/0.40 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.y $$unsorted) % 0.15/0.40 (declare-const tptp.function (-> $$unsorted Bool)) % 0.15/0.40 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 0.15/0.40 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.element_relation $$unsorted) % 0.15/0.40 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.universal_class $$unsorted) % 0.15/0.40 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.15/0.40 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.15/0.40 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.15/0.40 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.successor_relation $$unsorted) % 0.15/0.40 (declare-const tptp.choice $$unsorted) % 0.15/0.40 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.z $$unsorted) % 0.15/0.40 (declare-const tptp.subset_relation $$unsorted) % 0.15/0.40 (declare-const tptp.null_class $$unsorted) % 0.15/0.40 (declare-const tptp.x $$unsorted) % 0.15/0.40 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.omega $$unsorted) % 0.15/0.40 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.15/0.40 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.identity_relation $$unsorted) % 0.15/0.40 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.15/0.40 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.15/0.40 (define @t1 () (@var "Y" $$unsorted)) % 0.15/0.40 (define @t2 () (@var "U" $$unsorted)) % 0.15/0.40 (define @t3 () (@var "X" $$unsorted)) % 0.15/0.40 (define @t4 () (tptp.member @t2 @t3)) % 0.15/0.40 (define @t5 () (not @t4)) % 0.15/0.40 (define @t6 () (tptp.subclass @t3 @t1)) % 0.15/0.40 (define @t7 () (not @t6)) % 0.15/0.40 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 0.15/0.40 (define @t9 () (@list @t3 @t1)) % 0.15/0.40 (define @t10 () (@list @t3)) % 0.15/0.40 (define @t11 () (= @t3 @t1)) % 0.15/0.40 (define @t12 () (not @t11)) % 0.15/0.40 (define @t13 () (tptp.subclass @t1 @t3)) % 0.15/0.40 (define @t14 () (tptp.unordered_pair @t3 @t1)) % 0.15/0.40 (define @t15 () (not (tptp.member @t2 @t14))) % 0.15/0.40 (define @t16 () (or @t15 (= @t2 @t3) (= @t2 @t1))) % 0.15/0.40 (define @t17 () (forall (@list @t2 @t3 @t1) @t16)) % 0.15/0.40 (define @t18 () (not (tptp.member @t3 tptp.universal_class))) % 0.15/0.40 (define @t19 () (not (tptp.member @t1 tptp.universal_class))) % 0.15/0.40 (define @t20 () (tptp.singleton @t3)) % 0.15/0.40 (define @t21 () (tptp.ordered_pair @t3 @t1)) % 0.15/0.40 (define @t22 () (tptp.singleton @t1)) % 0.15/0.40 (define @t23 () (tptp.cross_product @t3 @t1)) % 0.15/0.40 (define @t24 () (@var "V" $$unsorted)) % 0.15/0.40 (define @t25 () (tptp.ordered_pair @t2 @t24)) % 0.15/0.40 (define @t26 () (tptp.member @t25 @t23)) % 0.15/0.40 (define @t27 () (not @t26)) % 0.15/0.40 (define @t28 () (@list @t2 @t24 @t3 @t1)) % 0.15/0.40 (define @t29 () (tptp.member @t24 @t1)) % 0.15/0.40 (define @t30 () (@var "Z" $$unsorted)) % 0.15/0.40 (define @t31 () (@list @t30 @t3 @t1)) % 0.15/0.40 (define @t32 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.15/0.40 (define @t33 () (tptp.member @t3 @t1)) % 0.15/0.40 (define @t34 () (tptp.member @t21 tptp.element_relation)) % 0.15/0.40 (define @t35 () (not (tptp.member @t21 @t32))) % 0.15/0.40 (define @t36 () (tptp.member @t30 @t3)) % 0.15/0.40 (define @t37 () (tptp.intersection @t3 @t1)) % 0.15/0.40 (define @t38 () (tptp.member @t30 @t37)) % 0.15/0.40 (define @t39 () (not @t38)) % 0.15/0.40 (define @t40 () (tptp.member @t30 @t1)) % 0.15/0.40 (define @t41 () (not @t36)) % 0.15/0.40 (define @t42 () (tptp.complement @t3)) % 0.15/0.40 (define @t43 () (tptp.member @t30 @t42)) % 0.15/0.40 (define @t44 () (@list @t30 @t3)) % 0.15/0.40 (define @t45 () (not (tptp.member @t30 tptp.universal_class))) % 0.15/0.40 (define @t46 () (tptp.complement (tptp.intersection @t42 (tptp.complement @t1)))) % 0.15/0.40 (define @t47 () (@var "Xr" $$unsorted)) % 0.15/0.40 (define @t48 () (tptp.restrict @t47 @t3 @t1)) % 0.15/0.40 (define @t49 () (tptp.domain_of @t3)) % 0.15/0.40 (define @t50 () (tptp.member @t30 @t49)) % 0.15/0.40 (define @t51 () (= (tptp.restrict @t3 (tptp.singleton @t30) tptp.universal_class) tptp.null_class)) % 0.15/0.40 (define @t52 () (tptp.cross_product @t32 tptp.universal_class)) % 0.15/0.40 (define @t53 () (tptp.rotate @t3)) % 0.15/0.40 (define @t54 () (@var "W" $$unsorted)) % 0.15/0.40 (define @t55 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t24 @t54) @t2) @t3)) % 0.15/0.40 (define @t56 () (tptp.ordered_pair @t25 @t54)) % 0.15/0.40 (define @t57 () (tptp.member @t56 @t53)) % 0.15/0.40 (define @t58 () (@list @t2 @t24 @t54 @t3)) % 0.15/0.40 (define @t59 () (not (tptp.member @t56 @t52))) % 0.15/0.40 (define @t60 () (tptp.flip @t3)) % 0.15/0.40 (define @t61 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t24 @t2) @t54) @t3)) % 0.15/0.40 (define @t62 () (tptp.member @t56 @t60)) % 0.15/0.40 (define @t63 () (@list @t1)) % 0.15/0.40 (define @t64 () (tptp.successor @t3)) % 0.15/0.40 (define @t65 () (= @t64 @t1)) % 0.15/0.40 (define @t66 () (tptp.member @t21 tptp.successor_relation)) % 0.15/0.40 (define @t67 () (tptp.member tptp.null_class @t3)) % 0.15/0.40 (define @t68 () (tptp.inductive @t3)) % 0.15/0.40 (define @t69 () (not @t68)) % 0.15/0.40 (define @t70 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 0.15/0.40 (define @t71 () (tptp.sum_class @t3)) % 0.15/0.40 (define @t72 () (@var "Yr" $$unsorted)) % 0.15/0.40 (define @t73 () (tptp.compose @t72 @t47)) % 0.15/0.40 (define @t74 () (tptp.member @t30 (tptp.image @t72 (tptp.image @t47 @t22)))) % 0.15/0.40 (define @t75 () (tptp.ordered_pair @t1 @t30)) % 0.15/0.40 (define @t76 () (tptp.member @t75 @t73)) % 0.15/0.40 (define @t77 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 0.15/0.40 (define @t78 () (tptp.single_valued_class @t3)) % 0.15/0.40 (define @t79 () (@var "Xf" $$unsorted)) % 0.15/0.40 (define @t80 () (tptp.subclass @t79 @t32)) % 0.15/0.40 (define @t81 () (tptp.function @t79)) % 0.15/0.40 (define @t82 () (not @t81)) % 0.15/0.40 (define @t83 () (@list @t79)) % 0.15/0.40 (define @t84 () (tptp.inverse @t79)) % 0.15/0.40 (define @t85 () (tptp.subclass (tptp.compose @t79 @t84) tptp.identity_relation)) % 0.15/0.40 (define @t86 () (tptp.regular @t3)) % 0.15/0.40 (define @t87 () (= @t3 tptp.null_class)) % 0.15/0.40 (define @t88 () (tptp.one_to_one @t79)) % 0.15/0.40 (define @t89 () (not @t88)) % 0.15/0.40 (define @t90 () (tptp.function @t84)) % 0.15/0.40 (define @t91 () (tptp.inverse tptp.element_relation)) % 0.15/0.40 (define @t92 () (tptp.operation @t79)) % 0.15/0.40 (define @t93 () (not @t92)) % 0.15/0.40 (define @t94 () (tptp.domain_of @t79)) % 0.15/0.40 (define @t95 () (tptp.domain_of @t94)) % 0.15/0.40 (define @t96 () (= (tptp.cross_product @t95 @t95) @t94)) % 0.15/0.40 (define @t97 () (tptp.subclass (tptp.range_of @t79) @t95)) % 0.15/0.40 (define @t98 () (@var "Xh" $$unsorted)) % 0.15/0.40 (define @t99 () (tptp.function @t98)) % 0.15/0.40 (define @t100 () (@var "Xf2" $$unsorted)) % 0.15/0.40 (define @t101 () (@var "Xf1" $$unsorted)) % 0.15/0.40 (define @t102 () (tptp.compatible @t98 @t101 @t100)) % 0.15/0.40 (define @t103 () (not @t102)) % 0.15/0.40 (define @t104 () (@list @t98 @t101 @t100)) % 0.15/0.40 (define @t105 () (tptp.domain_of @t101)) % 0.15/0.40 (define @t106 () (= (tptp.domain_of @t105) (tptp.domain_of @t98))) % 0.15/0.40 (define @t107 () (tptp.subclass (tptp.range_of @t98) (tptp.domain_of (tptp.domain_of @t100)))) % 0.15/0.40 (define @t108 () (tptp.operation @t101)) % 0.15/0.40 (define @t109 () (tptp.homomorphism @t98 @t101 @t100)) % 0.15/0.40 (define @t110 () (not @t109)) % 0.15/0.40 (define @t111 () (tptp.operation @t100)) % 0.15/0.40 (define @t112 () (tptp.not_homomorphism2 @t98 @t101 @t100)) % 0.15/0.40 (define @t113 () (tptp.not_homomorphism1 @t98 @t101 @t100)) % 0.15/0.40 (define @t114 () (tptp.ordered_pair @t113 @t112)) % 0.15/0.40 (define @t115 () (not @t111)) % 0.15/0.40 (define @t116 () (not @t108)) % 0.15/0.40 (define @t117 () (@list @t101 @t100 @t98)) % 0.15/0.40 (define @t118 () (tptp.member tptp.x tptp.z)) % 0.15/0.40 (define @t119 () (tptp.member tptp.y tptp.z)) % 0.15/0.40 (define @t120 () (tptp.unordered_pair tptp.x tptp.y)) % 0.15/0.40 (define @t121 () (tptp.subclass @t120 tptp.z)) % 0.15/0.40 (define @t122 () (@list @t120 tptp.z)) % 0.15/0.40 (define @t123 () (tptp.not_subclass_element @t120 tptp.z)) % 0.15/0.40 (define @t124 () (tptp.member @t123 tptp.z)) % 0.15/0.40 (define @t125 () (not @t124)) % 0.15/0.40 (define @t126 () (or @t125 @t121)) % 0.15/0.40 (define @t127 () (@list true false)) % 0.15/0.40 (define @t128 () (= tptp.x @t123)) % 0.15/0.40 (define @t129 () (not @t128)) % 0.15/0.40 (define @t130 () (not @t118)) % 0.15/0.40 (define @t131 () (not @t125)) % 0.15/0.40 (define @t132 () (= false true)) % 0.15/0.40 (define @t133 () (and @t118 @t128 @t125)) % 0.15/0.40 (define @t134 () (tptp.member @t123 @t120)) % 0.15/0.40 (define @t135 () (or @t134 @t121)) % 0.15/0.40 (define @t136 () (= tptp.y @t123)) % 0.15/0.40 (define @t137 () (not @t134)) % 0.15/0.40 (define @t138 () (or @t137 @t128 @t136)) % 0.15/0.40 (define @t139 () (@list false true false)) % 0.15/0.40 (define @t140 () (not @t136)) % 0.15/0.40 (define @t141 () (not @t119)) % 0.15/0.40 (define @t142 () (and @t119 @t136 @t125)) % 0.15/0.40 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 0.15/0.40 (assume @p2 (forall @t9 (or (tptp.member @t8 @t3) @t6))) % 0.15/0.40 (assume @p3 (forall @t9 (or (not (tptp.member @t8 @t1)) @t6))) % 0.15/0.40 (assume @p4 (forall @t10 (tptp.subclass @t3 tptp.universal_class))) % 0.15/0.40 (assume @p5 (forall @t9 (or @t12 @t6))) % 0.15/0.40 (assume @p6 (forall @t9 (or @t12 @t13))) % 0.15/0.40 (assume @p7 (forall @t9 (or @t7 (not @t13) @t11))) % 0.15/0.40 (assume @p8 @t17) % 0.15/0.40 (assume @p9 (forall @t9 (or @t18 (tptp.member @t3 @t14)))) % 0.15/0.40 (assume @p10 (forall (@list @t1 @t3) (or @t19 (tptp.member @t1 @t14)))) % 0.15/0.40 (assume @p11 (forall @t9 (tptp.member @t14 tptp.universal_class))) % 0.15/0.40 (assume @p12 (forall @t10 (= (tptp.unordered_pair @t3 @t3) @t20))) % 0.15/0.40 (assume @p13 (forall @t9 (= (tptp.unordered_pair @t20 (tptp.unordered_pair @t3 @t22)) @t21))) % 0.15/0.40 (assume @p14 (forall @t28 (or @t27 @t4))) % 0.15/0.40 (assume @p15 (forall @t28 (or @t27 @t29))) % 0.15/0.40 (assume @p16 (forall (@list @t2 @t3 @t24 @t1) (or @t5 (not @t29) @t26))) % 0.15/0.40 (assume @p17 (forall @t31 (or (not (tptp.member @t30 @t23)) (= (tptp.ordered_pair (tptp.first @t30) (tptp.second @t30)) @t30)))) % 0.15/0.40 (assume @p18 (tptp.subclass tptp.element_relation @t32)) % 0.15/0.40 (assume @p19 (forall @t9 (or (not @t34) @t33))) % 0.15/0.40 (assume @p20 (forall @t9 (or @t35 (not @t33) @t34))) % 0.15/0.40 (assume @p21 (forall @t31 (or @t39 @t36))) % 0.15/0.40 (assume @p22 (forall @t31 (or @t39 @t40))) % 0.15/0.40 (assume @p23 (forall @t31 (or @t41 (not @t40) @t38))) % 0.15/0.40 (assume @p24 (forall @t44 (or (not @t43) @t41))) % 0.15/0.40 (assume @p25 (forall @t44 (or @t45 @t43 @t36))) % 0.15/0.40 (assume @p26 (forall @t9 (= @t46 (tptp.union @t3 @t1)))) % 0.15/0.40 (assume @p27 (forall @t9 (= (tptp.intersection (tptp.complement @t37) @t46) (tptp.symmetric_difference @t3 @t1)))) % 0.15/0.40 (assume @p28 (forall (@list @t47 @t3 @t1) (= (tptp.intersection @t47 @t23) @t48))) % 0.15/0.40 (assume @p29 (forall (@list @t3 @t1 @t47) (= (tptp.intersection @t23 @t47) @t48))) % 0.15/0.40 (assume @p30 (forall (@list @t3 @t30) (or (not @t51) (not @t50)))) % 0.15/0.40 (assume @p31 (forall @t44 (or @t45 @t51 @t50))) % 0.15/0.40 (assume @p32 (forall @t10 (tptp.subclass @t53 @t52))) % 0.15/0.40 (assume @p33 (forall @t58 (or (not @t57) @t55))) % 0.15/0.40 (assume @p34 (forall (@list @t24 @t54 @t2 @t3) (or (not @t55) @t59 @t57))) % 0.15/0.40 (assume @p35 (forall @t10 (tptp.subclass @t60 @t52))) % 0.15/0.40 (assume @p36 (forall @t58 (or (not @t62) @t61))) % 0.15/0.40 (assume @p37 (forall (@list @t24 @t2 @t54 @t3) (or (not @t61) @t59 @t62))) % 0.15/0.40 (assume @p38 (forall @t63 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 0.15/0.40 (assume @p39 (forall (@list @t30) (= (tptp.domain_of (tptp.inverse @t30)) (tptp.range_of @t30)))) % 0.15/0.40 (assume @p40 (forall @t31 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t30 @t3 @t22) tptp.null_class)) (tptp.domain @t30 @t3 @t1)))) % 0.15/0.40 (assume @p41 (forall @t31 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t30 @t20 @t1) tptp.null_class)) (tptp.range @t30 @t3 @t1)))) % 0.15/0.40 (assume @p42 (forall (@list @t47 @t3) (= (tptp.range_of (tptp.restrict @t47 @t3 tptp.universal_class)) (tptp.image @t47 @t3)))) % 0.15/0.40 (assume @p43 (forall @t10 (= (tptp.union @t3 @t20) @t64))) % 0.15/0.40 (assume @p44 (tptp.subclass tptp.successor_relation @t32)) % 0.15/0.40 (assume @p45 (forall @t9 (or (not @t66) @t65))) % 0.15/0.40 (assume @p46 (forall @t9 (or (not @t65) @t35 @t66))) % 0.15/0.40 (assume @p47 (forall @t10 (or @t69 @t67))) % 0.15/0.40 (assume @p48 (forall @t10 (or @t69 @t70))) % 0.15/0.40 (assume @p49 (forall @t10 (or (not @t67) (not @t70) @t68))) % 0.15/0.40 (assume @p50 (tptp.inductive tptp.omega)) % 0.15/0.40 (assume @p51 (forall @t63 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 0.15/0.40 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 0.15/0.40 (assume @p53 (forall @t10 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t71))) % 0.15/0.40 (assume @p54 (forall @t10 (or @t18 (tptp.member @t71 tptp.universal_class)))) % 0.15/0.40 (assume @p55 (forall @t10 (= (tptp.complement (tptp.image tptp.element_relation @t42)) (tptp.power_class @t3)))) % 0.15/0.40 (assume @p56 (forall (@list @t2) (or (not (tptp.member @t2 tptp.universal_class)) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.15/0.40 (assume @p57 (forall (@list @t72 @t47) (tptp.subclass @t73 @t32))) % 0.15/0.40 (assume @p58 (forall (@list @t1 @t30 @t72 @t47) (or (not @t76) @t74))) % 0.15/0.40 (assume @p59 (forall (@list @t30 @t72 @t47 @t1) (or (not @t74) (not (tptp.member @t75 @t32)) @t76))) % 0.15/0.40 (assume @p60 (forall @t10 (or (not @t78) @t77))) % 0.15/0.40 (assume @p61 (forall @t10 (or (not @t77) @t78))) % 0.15/0.40 (assume @p62 (forall @t83 (or @t82 @t80))) % 0.15/0.40 (assume @p63 (forall @t83 (or @t82 @t85))) % 0.15/0.40 (assume @p64 (forall @t83 (or (not @t80) (not @t85) @t81))) % 0.15/0.40 (assume @p65 (forall (@list @t79 @t3) (or @t82 @t18 (tptp.member (tptp.image @t79 @t3) tptp.universal_class)))) % 0.15/0.40 (assume @p66 (forall @t10 (or @t87 (tptp.member @t86 @t3)))) % 0.15/0.40 (assume @p67 (forall @t10 (or @t87 (= (tptp.intersection @t3 @t86) tptp.null_class)))) % 0.15/0.40 (assume @p68 (forall (@list @t79 @t1) (= (tptp.sum_class (tptp.image @t79 @t22)) (tptp.apply @t79 @t1)))) % 0.15/0.40 (assume @p69 (tptp.function tptp.choice)) % 0.15/0.40 (assume @p70 (forall @t63 (or @t19 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 0.15/0.40 (assume @p71 (forall @t83 (or @t89 @t81))) % 0.15/0.40 (assume @p72 (forall @t83 (or @t89 @t90))) % 0.15/0.40 (assume @p73 (forall @t83 (or (not @t90) @t82 @t88))) % 0.15/0.40 (assume @p74 (= (tptp.intersection @t32 (tptp.intersection @t32 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t91)))) tptp.subset_relation)) % 0.15/0.40 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 0.15/0.40 (assume @p76 (forall (@list @t47) (= (tptp.complement (tptp.domain_of (tptp.intersection @t47 tptp.identity_relation))) (tptp.diagonalise @t47)))) % 0.15/0.40 (assume @p77 (forall @t10 (= (tptp.intersection @t49 (tptp.diagonalise (tptp.compose @t91 @t3))) (tptp.cantor @t3)))) % 0.15/0.40 (assume @p78 (forall @t83 (or @t93 @t81))) % 0.15/0.40 (assume @p79 (forall @t83 (or @t93 @t96))) % 0.15/0.40 (assume @p80 (forall @t83 (or @t93 @t97))) % 0.15/0.40 (assume @p81 (forall @t83 (or @t82 (not @t96) (not @t97) @t92))) % 0.15/0.40 (assume @p82 (forall @t104 (or @t103 @t99))) % 0.15/0.40 (assume @p83 (forall @t104 (or @t103 @t106))) % 0.15/0.40 (assume @p84 (forall @t104 (or @t103 @t107))) % 0.15/0.40 (assume @p85 (forall @t104 (or (not @t99) (not @t106) (not @t107) @t102))) % 0.15/0.40 (assume @p86 (forall @t104 (or @t110 @t108))) % 0.15/0.40 (assume @p87 (forall @t104 (or @t110 @t111))) % 0.15/0.40 (assume @p88 (forall @t104 (or @t110 @t102))) % 0.15/0.40 (assume @p89 (forall (@list @t98 @t101 @t100 @t3 @t1) (or @t110 (not (tptp.member @t21 @t105)) (= (tptp.apply @t100 (tptp.ordered_pair (tptp.apply @t98 @t3) (tptp.apply @t98 @t1))) (tptp.apply @t98 (tptp.apply @t101 @t21)))))) % 0.15/0.40 (assume @p90 (forall @t117 (or @t116 @t115 @t103 (tptp.member @t114 @t105) @t109))) % 0.15/0.40 (assume @p91 (forall @t117 (or @t116 @t115 @t103 (not (= (tptp.apply @t100 (tptp.ordered_pair (tptp.apply @t98 @t113) (tptp.apply @t98 @t112))) (tptp.apply @t98 (tptp.apply @t101 @t114)))) @t109))) % 0.15/0.40 (assume @p92 @t118) % 0.15/0.40 (assume @p93 @t119) % 0.15/0.40 (assume @p94 (not @t121)) % 0.15/0.40 (step @p95 :rule instantiate :premises (@p3) :args (@t122)) % 0.15/0.40 (step @p96 :rule cnf_or_pos :args (@t126)) % 0.15/0.40 (step @p97 :rule reordering :premises (@p96) :args ((or @t121 @t125 (not @t126)))) % 0.15/0.40 (step @p98 :rule chain_m_resolution :premises (@p97 @p94 @p95) :args (@t125 @t127 (@list @t121 @t126))) % 0.15/0.40 (step @p99 :rule eq-symm :args (@t2 @t1)) % 0.15/0.40 (step @p100 :rule eq-symm :args (@t2 @t3)) % 0.15/0.40 (step @p101 :rule refl :args (@t15)) % 0.15/0.40 (step @p102 :rule nary_cong :premises (@p101 @p100 @p99) :args (@t16)) % 0.15/0.40 (step @p103 :rule cong :premises (@p102) :args (@t17)) % 0.15/0.40 (step @p104 :rule eq_resolve :premises (@p8 @p103)) % 0.15/0.40 (step @p105 :rule instantiate :premises (@p104) :args ((@list @t123 tptp.x tptp.y))) % 0.15/0.40 (step @p106 :rule refl :args (@t129)) % 0.15/0.40 (step @p107 :rule bool-double-not-elim :args (@t124)) % 0.15/0.40 (step @p108 :rule refl :args (@t130)) % 0.15/0.40 (step @p109 :rule nary_cong :premises (@p108 @p107 @p106) :args ((or @t130 @t131 @t129))) % 0.15/0.40 (assume-push @p174 @t118) % 0.15/0.40 (assume-push @p175 @t128) % 0.15/0.40 (assume-push @p176 @t125) % 0.15/0.40 (step @p113 :rule evaluate :args (@t132)) % 0.15/0.40 (step @p114 :rule true_intro :premises (@p92)) % 0.15/0.40 (step @p115 :rule refl :args (tptp.z)) % 0.15/0.40 (step @p116 :rule symm :premises (@p175)) % 0.15/0.40 (step @p117 :rule cong :premises (@p116 @p115) :args (@t124)) % 0.15/0.40 (step @p118 :rule false_intro :premises (@p98)) % 0.15/0.40 (step @p119 :rule symm :premises (@p118)) % 0.15/0.40 (step @p120 :rule trans :premises (@p119 @p117 @p114)) % 0.15/0.40 (step @p121 false :rule eq_resolve :premises (@p120 @p113)) % 0.15/0.40 (step-pop @p177 :rule scope :premises (@p121)) % 0.15/0.40 (step-pop @p178 :rule scope :premises (@p177)) % 0.15/0.40 (step-pop @p179 :rule scope :premises (@p178)) % 0.15/0.40 (step @p122 :rule process_scope :premises (@p179) :args (false)) % 0.15/0.40 (assume-push @p180 @t118) % 0.15/0.40 (assume-push @p181 @t125) % 0.15/0.40 (assume-push @p182 @t128) % 0.15/0.40 (step @p129 :rule and_intro :premises (@p92 @p182 @p98)) % 0.15/0.40 (step-pop @p183 :rule scope :premises (@p129)) % 0.15/0.40 (step-pop @p184 :rule scope :premises (@p183)) % 0.15/0.40 (step-pop @p185 :rule scope :premises (@p184)) % 0.15/0.40 (step @p130 :rule process_scope :premises (@p185) :args (@t133)) % 0.15/0.40 (step @p134 :rule implies_elim :premises (@p130)) % 0.15/0.40 (step @p135 :rule resolution :premises (@p134 @p122) :args (true @t133)) % 0.15/0.40 (step @p136 :rule not_and :premises (@p135)) % 0.15/0.40 (step @p137 :rule eq_resolve :premises (@p136 @p109)) % 0.15/0.40 (step @p138 :rule chain_m_resolution :premises (@p137 @p92 @p98) :args (@t129 (@list false true) (@list @t118 @t124))) % 0.15/0.40 (step @p139 :rule instantiate :premises (@p2) :args (@t122)) % 0.15/0.40 (step @p140 :rule cnf_or_pos :args (@t135)) % 0.15/0.40 (step @p141 :rule reordering :premises (@p140) :args ((or @t121 @t134 (not @t135)))) % 0.15/0.40 (step @p142 :rule chain_m_resolution :premises (@p141 @p94 @p139) :args (@t134 @t127 (@list @t121 @t135))) % 0.15/0.40 (step @p143 :rule cnf_or_pos :args (@t138)) % 0.15/0.40 (step @p144 :rule reordering :premises (@p143) :args ((or @t137 @t128 @t136 (not @t138)))) % 0.15/0.40 (step @p145 :rule chain_m_resolution :premises (@p144 @p142 @p138 @p105) :args (@t136 @t139 (@list @t134 @t128 @t138))) % 0.15/0.40 (step @p146 :rule refl :args (@t140)) % 0.15/0.40 (step @p147 :rule refl :args (@t141)) % 0.15/0.40 (step @p148 :rule nary_cong :premises (@p147 @p107 @p146) :args ((or @t141 @t131 @t140))) % 0.15/0.40 (assume-push @p186 @t119) % 0.15/0.40 (assume-push @p187 @t136) % 0.15/0.40 (assume-push @p188 @t125) % 0.15/0.40 (step @p113 :rule evaluate :args (@t132)) % 0.15/0.40 (step @p152 :rule true_intro :premises (@p93)) % 0.15/0.40 (step @p115 :rule refl :args (tptp.z)) % 0.15/0.40 (step @p153 :rule symm :premises (@p187)) % 0.15/0.40 (step @p154 :rule cong :premises (@p153 @p115) :args (@t124)) % 0.15/0.40 (step @p118 :rule false_intro :premises (@p98)) % 0.15/0.40 (step @p119 :rule symm :premises (@p118)) % 0.15/0.40 (step @p155 :rule trans :premises (@p119 @p154 @p152)) % 0.15/0.40 (step @p156 false :rule eq_resolve :premises (@p155 @p113)) % 0.15/0.40 (step-pop @p189 :rule scope :premises (@p156)) % 0.15/0.40 (step-pop @p190 :rule scope :premises (@p189)) % 0.15/0.40 (step-pop @p191 :rule scope :premises (@p190)) % 0.15/0.40 (step @p157 :rule process_scope :premises (@p191) :args (false)) % 0.15/0.40 (assume-push @p192 @t119) % 0.15/0.40 (assume-push @p193 @t125) % 0.15/0.40 (assume-push @p194 @t136) % 0.15/0.40 (step @p164 :rule and_intro :premises (@p93 @p194 @p98)) % 0.15/0.40 (step-pop @p195 :rule scope :premises (@p164)) % 0.15/0.40 (step-pop @p196 :rule scope :premises (@p195)) % 0.15/0.40 (step-pop @p197 :rule scope :premises (@p196)) % 0.15/0.40 (step @p165 :rule process_scope :premises (@p197) :args (@t142)) % 0.15/0.40 (step @p169 :rule implies_elim :premises (@p165)) % 0.15/0.40 (step @p170 :rule resolution :premises (@p169 @p157) :args (true @t142)) % 0.15/0.40 (step @p171 :rule not_and :premises (@p170)) % 0.15/0.40 (step @p172 :rule eq_resolve :premises (@p171 @p148)) % 0.15/0.40 (step @p173 false :rule chain_m_resolution :premises (@p172 @p145 @p98 @p93) :args (false @t139 (@list @t136 @t124 @t119))) % 0.15/0.40 ) % 0.15/0.40 % SZS output end Proof % 0.15/0.41 % cvc5 exiting %------------------------------------------------------------------------------